Answer:
v < -18
Explanation:
You want the solution to -3(v +15) +1 > 10.
Simplify
Simplifying, we have ...
-3v -45 +1 > 10
-3v -44 > 10
Solve
Making the v-term positive, we get ...
-54 > 3v . . . . . . . . add 3v-10
-18 > v . . . . . . . divide by 3
The solution for v is v < -18.
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Additional comment
We could write the inequality as -3v > 54, then divide by -3. Doing that requires we reverse the inequality to v < -18. Sometimes that reversal is forgotten or confusing, so we choose to write the inequality in such a way that we don't need to reverse the symbol when we divide.
We like the final expression to involve the comparison symbols < or ≤, so the order of the variables and constants in that expression matches their order on the number line. Here, the variable v is on the left in v < -18, and the shaded portion is on the left of the boundary value -18 when we plot this on a number line.
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